The Pioneer Press spoke with Nelson Peterson ... who says, "All I can say is, we are asking for prayers and for respect for our family as we deal with this tragic situation."

8:41 AM PT -- Multiple sources with direct knowledge of the situation tell TMZ ... the injured child is Adrian's son, but it's not Adrian Peterson Jr., the child he's been famously photographed with in public over the years.

We reached out to Peterson's reps -- but so far, we have not heard back.

Adrian Peterson's 2-year-old son is currently in critical condition in a South Dakota hospital ... after he was allegedly severely beaten by the man dating the mother of his child, TMZ has learned.

The Minnesota Vikings running back immediately left his team to be with his son.

Officials tell us they've arrested the suspect, 27-year-old Joseph Patterson ... who's been charged with aggravated felony assault and battery of an infant.

According to law enforcement, emergency responders arrived to the apartment where Peterson's son was living at 5:46 PM on Wednesday ... and found the child unresponsive.

He was rushed to a nearby hospital and medical experts determined the injuries were consistent with abuse.

Law enforcement sources tell us ... the child suffered severe head injuries.

The suspect, Joseph Patterson, appeared in court just moments ago ... the judge set his bond at $750,000. Patterson tried desperately to shield his face from the cameras.